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**►****Foundations****▼****Algebra****►****11-XX Number theory****▼****12-XX Field theory and polynomials****►****12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****12Dxx Real and complex fields****►****12Exx General field theory****►****12Fxx Field extensions****►****12Gxx Homological methods (field theory)****►****12Hxx Differential and difference algebra****►****12Jxx Topological fields****►****12Kxx Generalizations of fields****►****12Lxx Connections with logic**- 12Y05 Computational aspects of field theory and polynomials

**►****13-XX Commutative rings and algebras****►****14-XX Algebraic geometry****►****15-XX Linear and multilinear algebra; matrix theory****►****16-XX Associative rings and algebras****►****17-XX Nonassociative rings and algebras****▼****18-XX Category theory; homological algebra****►****18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****▼****18Axx General theory of categories and functors**- 18A05 Definitions, generalizations
- 18A10 Graphs, diagram schemes, precategories
- 18A15 Foundations, relations to logic and deductive systems
- 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
- 18A22 Special properties of functors (faithful, full, etc.)
- 18A23 Natural morphisms, dinatural morphisms
- 18A25 Functor categories, comma categories
- 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
- 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams
- 18A35 Categories admitting limits (complete categories), functors preserving limits, completions
- 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
- 18A99 None of the above, but in this section

**►****18Bxx Special categories****►****18Cxx Categories and theories****▼****18Dxx Categories with structure**- 18D05 Double categories,
*2*-categories, bicategories and generalizations - 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
- 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
- 18D20 Enriched categories (over closed or monoidal categories)
- 18D25 Strong functors, strong adjunctions
- 18D30 Fibered categories
- 18D35 Structured objects in a category (group objects, etc.)
- 18D50 Operads
- 18D99 None of the above, but in this section

- 18D05 Double categories,
**►****18Exx Abelian categories****►****18Fxx Categories and geometry****▼****18Gxx Homological algebra**- 18G05 Projectives and injectives
- 18G10 Resolutions; derived functors
- 18G15 Ext and Tor, generalizations, Künneth formula
- 18G20 Homological dimension
- 18G25 Relative homological algebra, projective classes
- 18G30 Simplicial sets, simplicial objects (in a category)
- 18G35 Chain complexes
- 18G40 Spectral sequences, hypercohomology
- 18G50 Nonabelian homological algebra
- 18G55 Homotopical algebra
- 18G60 Other (co)homology theories
- 18G99 None of the above, but in this section

**▼****19-XX***K*-theory**►****19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****19Axx Grothendieck groups and***K*_{0}**►****19Bxx Whitehead groups and***K*_{1}**►****19Cxx Steinberg groups and***K*_{2}**►****19Dxx Higher algebraic***K*-theory**►****19Exx***K*-theory in geometry**►****19Fxx***K*-theory in number theory**►****19Gxx***K*-theory of forms**►****19Jxx Obstructions from topology****►****19Kxx***K*-theory and operator algebras**►****19Lxx Topological***K*-theory- 19M05 Miscellaneous applications of
*K*-theory

**▼****20-XX Group theory and generalizations****►****20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****20Axx Foundations****►****20Bxx Permutation groups****▼****20Cxx Representation theory of groups**- 20C05 Group rings of finite groups and their modules
- 20C07 Group rings of infinite groups and their modules
- 20C08 Hecke algebras and their representations
- 20C10 Integral representations of finite groups
- 20C11
*p*-adic representations of finite groups - 20C12 Integral representations of infinite groups
- 20C15 Ordinary representations and characters
- 20C20 Modular representations and characters
- 20C25 Projective representations and multipliers
- 20C30 Representations of finite symmetric groups
- 20C32 Representations of infinite symmetric groups
- 20C33 Representations of finite groups of Lie type
- 20C34 Representations of sporadic groups
- 20C35 Applications of group representations to physics
- 20C40 Computational methods
- 20C99 None of the above, but in this section

**►****20Dxx Abstract finite groups****►****20Exx Structure and classification of infinite or finite groups****►****20Fxx Special aspects of infinite or finite groups****▼****20Gxx Linear algebraic groups (classical groups)**- 20G05 Representation theory
- 20G10 Cohomology theory
- 20G15 Linear algebraic groups over arbitrary fields
- 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
- 20G25 Linear algebraic groups over local fields and their integers
- 20G30 Linear algebraic groups over global fields and their integers
- 20G35 Linear algebraic groups over adčles and other rings and schemes
- 20G40 Linear algebraic groups over finite fields
- 20G42 Quantum groups (quantized function algebras) and their representations
- 20G45 Applications to physics
- 20G99 None of the above, but in this section

**►****20Hxx Other groups of matrices****►****20Jxx Connections with homological algebra and category theory****►****20Kxx Abelian groups**- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
**►****20Mxx Semigroups****►****20Nxx Other generalizations of groups**- 20P05 Probabilistic methods in group theory

**►****Analysis****►****Differential Equations****►****Transformations****►****Geometry****▼****Statistics****►****Applied Mathematics****►****Didactics**

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